Generation of various kinds of signals using a Fourier transform is widely performed, for example, in the image processing field, various kinds of measurement fields, and the audio analysis field.
For example, an optical coherence tomography imaging apparatus (Fourier Domain—Optical Coherence Tomography: FD-OCT) is used which obtains a tomographic information signal of a measurement target by performing a Fourier transform on an optical spectral interference signal.
In FD-OCT, light source output is divided into two or more beams, one of which is used as reference light and another of which is used as measurement light with which the measurement target is irradiated. Scattered or reflected light is returned back from the measurement target, and an optical spectral interference signal between the scattered or reflected light and the above-described reference light is obtained. The optical spectral interference signal is observed along the wave-number space axis, and a signal is obtained which vibrates along the wave-number space axis in accordance with the difference in optical path length between the reference light path and the measurement light path. Accordingly, the obtained optical spectral interference signal is subjected to a Fourier transform so that a tomographic information signal is obtained which indicates a peak in accordance with the difference in optical path length.
The intensity of the optical spectral interference signal is proportional to the product of the intensities of the reference light and the feedback light from the measurement target. Therefore, even when the feedback light from the measurement target is attenuated due to absorption, scattering, or transmission, a tomographic information signal of high sensitivity can be obtained.
A tomographic information signal obtained by performing a Fourier transform on an optical spectral interference signal represents the result of convolution calculation of a Fourier transform signal of a sine wave having a frequency based on the difference in optical path length and a shape obtained by performing a Fourier transform on the spectral shape.
Therefore, as the spectral band (e.g., depending on the wavelength band of the light source) is wider, a tomographic information signal having a higher resolution in the depth direction (ability to resolve a layer structure and display it) is obtained.
However, a spectral band is generally finite, and a spectral shape has a certain shape. Therefore, the shape of a tomographic information signal reflects the shape obtained by performing a Fourier transform on the spectral shape. Thus, degradation of a tomographic information signal occurs, such as in the case of an image display in which a tomographic layer which is originally one layer is displayed as multiple layers, a display in which multiple layers are not separated and are displayed as one layer, or a state in which a tomographic information signal of small intensity is buried at a tail of a tomographic information signal of large intensity.
Therefore, to suppress the degradation of a tomographic information signal, a method has been employed in which an obtained optical spectral interference signal is multiplied by a window function so that the waveform is shaped, in order to shape the tomographic information signal. This method causes a tomographic information signal to be made unimodal, and achieves suppression of noise. However, multiplication of a window function causes the optical spectral band to be narrowed, and causes the width of the tomographic information signal to be increased, resulting in degradation of the resolution in the depth direction of the tomographic image.
Such degradation of a signal is not limited to optical tomographic layer measurement, and is a common issue for signal processing or signal analysis processing accompanying a Fourier transform.
To solve the above-described issue, in the case of radar or the like, a method, for example, as in PTL 1 has been proposed which is called super spatially variant apodization and in which multiple extrapolations and resolution beyond the limits of diffraction are performed. In this method, a waveform is extracted in a wide band, the center of which is at a peak of a signal which is subjected to a Fourier transform, and an inverse Fourier transform is performed on the extracted waveform so that an extrapolation signal is generated. Then, the extrapolation signal is extrapolated to the original waveform so as to improve the resolution. By repeatedly performing this signal processing, a signal of higher resolution is obtained.
In the audio analysis-synthesis field as well, a method, for example, as in PTL 2, has been proposed in which frequency analysis is performed so that a signal is synthesized from the analysis result. In this method, only a main frequency component is extracted, and phase correction is performed so that sound is synthesized.